Mass-change And Geosciences International Constellation (MAGIC) expected impact on science and applications

Geophys. J. In . (2024) 236, 1288–1308 h ps://doi.o g/10.1093/gji/ggad472 Ad ance Access publica ion 2023 Decembe 14 GJI G a i y, Geodesy and Tides Mass-change And Geosciences In e na ional Cons ella ion (MAGIC) expec ed impac on science and applica ions I. Da as , 1 G. Ma ch, 2 R. Pail , 3 C. W. Hughes , 4 , 5 C. B ai enbe g, 6 A. G ¨ un ne , 7 , 8 A. Eicke , 9 B. Wou e s, 10 B. Helle -Kaiko , 3 T. Pi e a 6 and A. Pas o u i 6 1 Eu opean Space Agency, Ea h & Mission Science Di ision, ESTEC, 2201 AZ Noo dwijk, The Ne he lands. E-mail: ilias.da [email p o ec ed] 2 RHEA o Eu opean Space Agency, Ea h & Mission Science Di ision, ESTEC, 2201 AZ Noo dwijk, The Ne he lands 3 Ins i u e o As onomical and Physical Geodesy, Technical Uni e si y o Munich (TUM), A ciss aße 21 , D-80333 M ¨ unchen, Ge many 4 School o En i onmen al Sciences, Uni e si y o Li e pool, L 3 5 DA Li e pool, UK 5 Na ional Oceanog aphy Cen e, L 3 5 DA Li e pool, UK 6 Depa men o Ma hema ics and Geosciences, Uni e si y o T ies e, Via Weiss 1 , I-34128 T ies e, I aly 7 Helmhol z Cen e Po sdam, GFZ Ge man Resea ch Cen e o Geosciences, 14476 Po sdam, Ge many 8 Ins i u e o En i onmen al Sciences and Geog aphy, Uni e si y o Po sdam, 14473 Po sdam, Ge many 9 Ha enCi y Uni e si y Hambu g, 20457 Hambu g, Ge many 10 Depa men o Geoscience and Remo e Sensing, Del Uni e si y o Technology, 2628 CN Del , The Ne he lands Accep ed 2023 Decembe 4. Recei ed 2023 Decembe 3; in o iginal o m 2023 Ap il 18 S U M M A R Y The join ESA/NASA Mass-change And Geosciences In e na ional Cons ella ion (MAGIC) has he objec i e o ex end ime-se ies om p e ious g a i y missions, including an imp o e- men o accu acy and spa io- empo al esolu ion. The long- e m moni o ing o Ea h’s g a i y ield ca ies in o ma ion on mass change induced by wa e cycle, clima e change and mass anspo p ocesses be ween a mosphe e, c yosphe e, oceans and solid Ea h. MAGIC will be composed o wo sa elli e pai s lying in di e en o bi planes. The NASA/DLR-led i s pai (P1) is expec ed o be in a nea -pola o bi a ound 500 km o al i ude; while he second ESA-led pai (P2) is expec ed o be in an inclined o bi o 65 ◦–70 ◦a app oxima ely 400 km al i ude. The ESA-led pai P2 Nex Gene a ion G a i y Mission shall be launched a e P1 in a s agge ed manne o o m he MAGIC cons ella ion. The addi ion o an inclined pai shall lead o educ ion o empo al aliasing e ec s and consequen ly o eliance on de-aliasing models and pos -p ocessing. The main no el y o he MAGIC cons ella ion is he deli e y o mass-change p oduc s a highe spa ial esolu ion, empo al (i.e. subweekly) esolu ion, sho e la ency and highe accu acy han he G a i y Reco e y and Clima e Expe imen (GRACE) and G a i y Reco e y and Clima e Expe imen Follow-On (GRACE-FO). This will pa e he w ay o ne w science applica ions and ope a ional se ices. In his pape , an o e iew o a ious ields o science and se ice applica ions o hyd olo gy, c yosphe e, oceano g aphy, solid Ea h, clima e change and geodesy is p o ided. These hema ic ields and ne wl y enabled applica- ions and se ices we e analysed in he ame o he ini ial ESA Science Suppo ac i i ies o MAGIC. The analyses o MAGIC scena ios o di e en applica ion a eas in he ield o geosciences con i med ha he double-pai con igu a ion will signi ican ly enla ge he numbe o obse able mass-change phenomena by esol ing smalle spa ial scales wi h an unce ain y ha sa is ies e ol ed use equi emen s exp essed by in e na ional bodies such as IUGG. The equi ed unce ain y le els o dedica ed hema ic ields me by MAGIC un il e ed Le el-2 p oduc s will bene i hyd ological applica ions by eco e ing mo e han 90 pe cen o he ma- jo i e basins wo ldwide a 260 km spa ial esolu ion, c yosphe e applica ions by enabling mass change signal sepa a ion in he in e io o G eenland om hose in he coas al zones and by esol ing small-scale mass a iabili y in challenging egions such as he An a c ic Penin- sula, oceanog aphy applica ions by moni o ing me idional o e u ning ci cula ion changes on imescales o yea s and decades, clima e applica ions by de ec ing ampli ude and phase changes o Te es ial Wa e S o age a e 30 y in 64 and 56 pe cen o he global land a eas 1288 C The Au ho (s) 2024. Published by Ox o d Uni e si y P ess on behal o The Royal As onomical Socie y. This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License ( h ps://c ea i ecommons.o g/licenses/by/4.0/ ), which pe mi s un es ic ed euse, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1289 and solid Ea h applica ions by lowe ing he Ea hquake de ec ion h eshold om magni ude 8.8 o magni ude 7.4 wi h spa ial esolu ion inc eased o 333 km. Key wo ds: Global change om geodesy; Sa elli e g a i y; Time a iable g a i y; Glaciol- o gy; Hyd olo gy; Ea hquake dynamics. 1 INTRODUCTION Con inui y and e olu ion o g a i y missions o obse e mass change is o eseen a ound he u n o his decade in o de o mee p io i y use needs no add essed by he exis ing and planned sa el- li e in as uc u e. The global scien i ic use communi y has been con inuously add essing he need o enhanced and sus ained mass- change moni o ing om space, ia bodies such as he Global Geode- ic Obse ing Sys em, In e na ional Associa ion o Geodesy and he In e na ional Union o Geodesy and Geophysics (IUGG) (IUGG 2015 Resolu ion no. 2 2015 ), (IUGG 2023 Resolu ion no. 2, 2023 ). P edecesso g a i y missions like he Challenging Minisa elli e Pay- load (CHAMP) (Reigbe e al. 2002 ), G a i y Reco e y and Cli- ma e Expe imen (GRACE) (Tapley e al. 2004 ), G a i y Field and s eady-s a e Ocean Ci cula ion (GOCE) (D inkwa e e al. 2003 ) and GRA CE Follo w-On (Lande e e al. 2020 ) ha e e olu ionize ou unde s anding o he global s a ic and empo al a ying g a - i y ield and he ela ed moni o ing o mass anspo p ocesses, bu also showed limi a ion ega ding he achie able spa ial and empo al esolu ion o esul ing g a i y ield p oduc , o example, Thomas e al. (2017 ), Rodell e al. ( 2018 ), Cazena e e al. ( 2019 ), Wou e s e al. ( 2019 ) and Ci ac ` ıe al. ( 2020 ). A new mission o imp o e he moni o ing o hyd ology, c yosphe e, oceanog aphy, solid Ea h and clima e change is he e- o e s ongly an icipa ed. This e olu ion will p o ide enhanced con- inui y o science and se ices wi h espec o imp o ing upon cu - en capabili ies and enabling no el science, applica ions and se - ices. Achie ing accu a e pu ely sa elli e-based solu ions on daily o weekly imescales was no possible wi h he p e ious gene a ion o g a i y missions. Indeed, a he momen his is onl y achie - able in combina ion wi h models (C o eau e al. 2020 ). The Mass- change And Geosciences In e na ional Cons ella ion (MAGIC), a collabo a ion be ween he Eu opean Space Agency (ESA) and he Na ional Ae onau ics and Space Adminis a ion (NASA) ini ia ed o e a decade ago, aims a ul illing his new objec i e o imp o e cu en models and moni o ing and in pa icula o in oduce he ca- pabili y o moni o and o ecas ex eme e en s like loods, d ough s and o he na u al haza ds. The Eu opean Nex -Gene a ion G a i y Mission (NGGM), pa o MAGIC, is cu en ly in i s Phase A Ex ension as i s Mission o Oppo uni y in he ESA’s Fu u eEO P og amme. In he ame o he in e na ional coope a ion, ESA and NASA ha e coo dina ed s udies on g a i y cons ella ions o op imize he e ie al o mass change and anspo in he Ea h sys em. The new high spa io- empo al esolu ions enable no el applica ions wi h he possibili y o achie e sho - e m (o as - ack) g a i y p oduc s in a subweekly basis. The collabo a ion aims a ul illing he needs o in e na ional use s communi ies, which a e well exp essed in he IUGG epo om 2015 (Pail e al. 2015 ). The ESA/NASA Ad-hoc Join Sci- ence S udy Team con ibu ed o he consolida ion o mission e- qui emen s o he join ESA/NASA MAGIC Mission Requi emen s Documen (MRD, Haagmans & Tsaoussi 2020 ), whe e ecommen- da ions om he 2015 IUGG epo (Pail e al. 2015 ) and he 2017 US Decadal Su e y (Decadal Su e y, 2017 ) we e adop ed. Fu he ecommenda ions based on p e ious wo k and s udies (e.g. Bende e al. 2008 ; I an Pou e al. 2015 ; Pail e al. 2019 ; Pu khause e al. 2020 ), N ASA/ESA In e agency G a i y Science Wo king G oup (Visse e al. 2016 ) and he la es ad ances in sa elli e g a ime y we e also inco po a ed in he MAGIC MRD. The i s pai (P1) o he MAGIC Cons ella ion will be imple- men ed ia a NASA/Ge man Ae ospace Cen e (DLR) as -paced coope a ion o ensu e con inui y o obse a ions. The second pai (P2) will be implemen ed by ESA, possibly wi h some NASA con ibu ions. A s agge ed launch app oach o he wo sa elli e pai s should p o ide a leas 4 y o combined ope a ions o MAGIC (Haagmans & Tsaoussi 2020 ). On NASA side, a Phase A s udy was ini ia ed in 2023 Ma ch. On ESA side, since 2020 he NGGM/MAGIC concep is in es iga ed in wo pa allel indus- ial Phase A s udies complemen ed by a science suppo s udy h ps://www.asg.ed. um.de/en/iapg/magic/ . In he ame o he la - e , se e al po en ial a chi ec u es and mission scena ios we e in es- iga ed and nume ically simula ed o maximize he MAGIC’s scien- i ic e u n. The Bende - ype double-pai mission concep (Bende e al. , 2008 ) and single/mul iple pendulum con igu a ions (Elsaka e al. 2013 ) we e simula ed in g ea dep h. In hese simula ions, eal- is ic e o assump ions ega ding he key payload p oduc s, in close in e ac ion wi h he wo pa allel indus y s udies, we e also imple- men ed. In he ame o he science suppo ac i i ies o MAGIC, me hodological imp o emen s o p ocessing s a egies, op imum ea men o long- e m signals and ailo ed pos -p ocessing ech- niques we e also analysed (Ab ykoso e al. 2021 , 2022 ; Helle - Kaiko e al. 2023 ). The esul ing simula ions p o ided a clea o e iew on mission pe o mance and scien i ic imp o emen s en- abled by MAGIC. Beyond he desc ip ion o simula ions se up and hei imp o emen , which is a ailable in Helle -Kaiko e al. ( 2023 ), his pape summa izes he ini ial esul s and ecommen- da ions om he ESA science s udy, and ocuses on he scien i ic applica ions and he imp o emen s expec ed o be achie ed wi h MAGIC. A b ie in oduc ion on analysed cons ella ion scena ios and adop ed me hodology is gi en in Sec ions 2 and 3 , espec i ely. In Sec ion 4 , he main esul s and compa isons wi h he MAGIC MRD equi emen s a e shown and discussed. Sec ion 5 p esen s he sci- en i ic impac and applica ions o e a se o speci ic hema ic ields: hyd olo gy, c yosphe e, oceano g aphy, solid Ea h, clima e-change and geodesy. Conclusions and ecommenda ions o ongoing and u u e wo k a e inally p o ided in Sec ion 6 . I should be no ed ha , as esul o echnical and p og amma ic cons ain s, he cu en as- sump ion o he MAGIC o bi s is somewha di e en han he cases p esen ed in his pape and ongoing s udies add ess such o bi con- igu a ion. Ho we e , he esul s p esen ed a e ully applicable bu o mino aspec s ha will be desc ibed in la e publica ions. 2 CONSTELLATION SCENARIOS In he ESA Science Suppo s udy, he analysed o bi s a e based on he o iginal candida e o bi s p o ided in Masso i e al. ( 2021 ) and on a ew addi ional scena ios which will be discussed he e- Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1290 I. Da as e al . a e . The main a en ion is o en ocused on he so-called 3d H scena io, which is de ined by a pola pai a 463 km mean al i ude and 89 ◦inclina ion, and a second pai a 432 km mean al i ude and 70 ◦inclina ion. The ull lis o analysed o bi s is a ailable in Appendix A . To s udy he impac o di e en pe iods o nea e- pea o bi s, o subcycles, and he in luence o a change o al i ude, se e al scena ios we e de ined. Beyond he Bende con igu a ions, a ew Sun-synch onous o bi (SSO) and pendulum concep s we e also in oduced. Fo all sa elli e pai s, he nominal in e sa elli e dis- ance (ISD) baseline leng h is se o 220 km. Fo he scena ios 3d H and 5d LL addi ional sa elli e andems we e analysed, including in- line andems wi h a baseline leng h o 100, 150 and 180 km, and pendulum pai s wi h angles o 15 ◦, 30 ◦and 45 ◦. Se e al po en ial mission a chi ec u es we e in es iga ed o na - o w do wn he ade space o he cons ella ion, especially o p o ide eedback o he pa allel Phase A sys em indus y s udies, and o iden i y an op imum se -up ega ding science e u n, echnical ea- sibili y and cos s. 3 METHODOLOGY The nume ical closed-loop simula ions pe o med o e alua e he compliance o a ious mission a chi ec u es o he gi en use e- qui emen s and hei impac on applica ions a e based on he ull- scale g a i y simula ion so wa e a he Ins i u e o As onomical and Physical Geodesy (IAPG), which is desc ibed in de ail in Da as e al. ( 2015 ) and Da as ( 2016 ). The se -up o hese simula ions is desc ibed in de ail in Helle -Kaiko e al. ( 2023 ) as summa ized b ie ly in wha ollows. As a i s s ep, o bi s o he in ol ed sa elli es a e compu ed a a sampling a e o 5 s. The o bi scena ios unde - lying he simula ions a e summa ized in he Table A1 in Appendix A . All o bi s ha e speci ic subcycles: a e a p e-de ined pe iod o ime, he sa elli es come close o hei ini ial (Ea h- ixed) posi ion, wi h a longi udinal shi as speci ied in he able, hus gene a ing a homogeneous g ound- ack pa e n wi hin a gi en subcycle. All simula ions e e o he pe iod o ime s a ing a 2002 Janua y 1. Depending on he speci ic anal ysis, mon hl y (31 d), weekly (7 d) o sho - e m (3 d) solu ions a e compu ed. No mal equa ions a e assembled and sol ed up o a maximum sphe ical ha monic (SH) deg ee/o de (d/o) o 120, 100 o 70, depending on he e ie al pe iod. Rega ding o ce (backg ound) models in he closed-loop simu- la ion, we dis inguish be ween models used o o wa d modelling (‘ ue wo ld’), ha is, compu a ion o he o bi s and simula ion o he obse a ions, and he g a i y e ie al (‘ e e ence wo ld’), ha is, se -up o obse a ion equa ions and obse a ion esiduals. Fo he o wa d modelling, he ocean ide model EOT11a (Sa cenko & Bosch 2012 ) and he ull a mosphe e, ocean, hyd ology, ice and solid Ea h (AOHIS) signal gi en by he upda ed Ea h Sys em Model o ESA (Dobslaw e al. 2015 ) a e used. Fo he compu a- ion o e e ence obse a ions, he ocean ide model GOT4.7 (Ray 2008 ) is applied, meaning ha we use he di e ence o he wo ocean ide models EOT11a and GOT4.7 as a measu e o he ocean ide backg ound model e o . In he case o he nominal p ocessing scheme, he a mosphe e and ocean (AO)-de-aliasing p oduc and he co esponding e o es ima es (Dobslaw e al. 2016 ) a e used in he in e sion, such ha −"Hyd ology, Ice and Solid Ea h −" HIS signals a e e ie ed. In bo h o wa d and backwa d modelling, he s a ic g a i y ield model GOCO05s (May e -G ¨ u e al. 2015 ) is used, assuming ha i is pe ec ly known. All backg ound models ex end up o d/o 120. F om he simula ed o bi s, syn he ic High-Low (HL) and Low- Low (LL) Sa elli e- o-Sa elli e T acking (SST) obse a ions and esidual obse a ions a e compu ed, using e e ence o ce models as desc ibed abo e. P oduc -noise models o he key ins umen s, lase anging in e e ome e , accele ome e s (ACC) and Global Na i- ga ion Sa elli e Sys ems (GNSS) ecei e a e supe imposed ( hei models a e assumed o include he e ec s o all he in e ac ions wi h he sa elli e, e.g. hose wi h es ima ion and con ol sys ems o a i ude and he mal s abiliza ion). These noise models a e de- ined by Helle -Kaiko e al. ( 2023 , ch. 2.1.2). The SH coe icien s a e e ie ed by means o a s anda d leas -squa es pa ame e ad- jus men based on a Gauss–Ma ko model. The s ochas ic model is de i ed om p e- i esiduals o p oduc -only noise simula ions. The e o e, i is composed only o ins umen e o s and does no con ain modelled empo al aliasing e ec s. The e ie al e o  x = x −x HIS cha ac e izing he g a i y e ie al pe o mance o he conside ed simula ed mission se up is compu ed as di e ence o he e ie ed SH coe icien s x and he SH coe icien s x HIS o he unde lying ‘ ue’ mean HIS signal o he espec i e pe iod o ime. In o de o isualize and compa e he global e ie al pe o mance o se e al scena ios, we compu e he deg ee ampli udes o hei e ie al e o s  c nm and  s nm in uni s o equi alen w a e heigh (EWH, Wah e al. 1998 ) acco ding o σ( n ) = aρe 3 ρw 2 n + 1 1 + k n     n  m = 0 c 2 nm + s 2 nm , (1) whe e a is he semimajo axis o he Ea h ellipsoid, ρe he mean densi y o Ea h, ρw he densi y o wa e , k n a e he Lo e numbe s and n and m ep esen he SH deg ee and o de . De ailed nume ical s udies ha e shown ha he esul ing pe o - mance scales wi h he e ie al pe iod, espec i el y, he numbe o unde l ying obse a ions N acco ding o he Gaussian e o p opa- ga ion ule o √ N . This does no only hold o p oduc -only e o cases including sys em measu emen e o s only, bu also o he ull-noise cases including also empo al aliasing e o s (Pail e al. 2022 ). 4 RESULTS AND MATCH AGAINST MAGIC REQUIREMENTS Fig. 1 shows a pe o mance o e iew o he di e en cons ella ion designs o a eco e y pe iod o 31 d as de ined in Table A1 o Appendix A. These esul s, which a e mainly based on he 3d H scena io including ealis ic e o models o he key ins umen s and idal and non- idal backg ound model e o s ( c . Sec ion 3 ), clea ly demons a e he supe io pe o mance o Bende double- pai mission concep s o e all o he po en ial cons ella ions, such as single-pai inline, SSO, o pendulum a chi ec u es. In case whe e he esul s include all e o sou ces a e labelled as ‘ ull noise’, whe eas in case idal and non- idal backg ound model e o s a e omi ed hey a e labelled as ‘p oduc -only’ solu ions. A his poin i is o men ion ha ollowing he app oach om ESA NGGM and MAGIC MRD documen s (Haagmans & Tsaoussi 2020 ), we use in his s udy un il e ed solu ions as a pe o mance me ic. Any pos -p ocessing op ion would a ec he mission pe - o mance in a di e en manne (di e en handling o omission and commission e o , di e en leakage and smoo hing e ec s, di e en signal dampening e ec s). The e o e, we conside he use o un il- e ed solu ions as he mos unambiguous s a egy. I is e iden , ha he di e ence be ween a single- and a double-pai solu ion will be Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1291 0 20406080100120 10 -2 10 -1 10 0 10 1 mean HIS signal in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) MARVEL 3 sa . Bende : pol. (G), incl. (N) Bende : bo h pend. (G/N) pol. + sun-sync. (G/N) Bende : incl. low (G/N) Bende : pol. + incl. low (N/N) Figu e 1. Deg ee e o ampli udes o 31-d ull-noise solu ions om a ious mission cons ella ions. ‘G’ means ‘Supe S a ’ (GRACE- ype) and N ‘Mic oS a ’ (NGGM/MA GIC- ype) A CC pe o mance. The numbe s ‘15 ◦’ and ‘30 ◦’ e e o he opening angle o he pendulum o ma ion. la ges o un il e ed solu ions, because any ype o il e ing will a - enua e he ad an age o double pai s ega ding hei inc eased spa- ial and empo al esolu ion and hei in insic imp o ed de-aliasing capabili ies. Impac s udies based on pos -p ocessed solu ion s we e pe o med, o example, by Hauk & Wiese ( 2020 ) and Wiese e al. ( 2022 ). On op o p e iousl y men ioned bene i s o lying in a Bende cons ella ion, he al i ude emains he main pe o mance d i e . In addi ion, in a double-pai scena io, he ela i e con ibu ion o he inclined pai o he o al pe o mance is mo e han 90 pe cen in he a eas co e ed by bo h pai s (Pail e al. 2022 ; Zhou e al. 2021 ). The e o e, a low al i ude oge he wi h high-pe o mance ins umen a ion o he inclined pai is absolu ely essen ial (Pail e al. 2022 ). The Science Suppo S udy in he MAGIC Phase A has also analysed di e en ISD choices be ween sa elli es o he same pai . This dis ance ep esen s a comp omise be ween sensi i - i y (which imp o es wi h a longe dis ance) and spa ial esolu ion (which deg ades wi h g ea e dis ances). Based on pe o med sim- ula ions (Pail e al. 2022 ), ISD has an op imum o a dis ance o 200–250 km. Fo his eason, i is ecommended o each pai o ly wi h in-line o ma ions sepa a ed by 220 km, simila as ealized on GRACE and GRACE-FO. The simula ed Le el-2 g a i y solu ions demons a e a p o- nounced gain using a double pai wi h espec o single pai GRACE- ype scena ios, as no able in Fig. 2 , showing he imp o emen a ios wi h espec o single pai . The g ea es imp o emen can be seen o he ‘LL’ scena io (5d LL, also labelled as ‘Bende : pol. + incl. low ( N / N )’). This comes as an ou come o he al i ude choice being he lowes among he ep esen ed a chi ec u es. Abo e SH deg ee 40–50, o mos o he al e na i e scena ios, imp o emen s can go beyond 10 imes highe han single-pai GRACE- ype con igu a- ions o high-al i udes scena ios. In he coe icien band a ound SH deg ee 80, whe e he signal- o-noise a io (SNR) is close o one o wo-pai cons ella ions, he imp o emen s a e a ound 30 o Ben- de in-line scena io 3d H compa ed o single-pai GRACE- ype con igu a ions. The Le el-2 mission pe o mance o di e en a chi ec u es is compa ed agains use equi emen s summa ized in he MAGIC MRD (Haagmans & Tsaoussi 2020 ). Fig. 3 depic s he cumula i e RMS cu es o mon hly ull-noise solu ions, w hile F ig. 4 o he p oduc -only solu ions. The p oduc -only case includes he con i- bu ion o he measu emen sys em e o , which is de ined as he unce ain y o Le el-2 g a i y ield p oduc s solely esul ing om sa elli e ins umen inaccu acies and hei coupling e ec s a sa el- li e (o cons ella ion) le el bu excluding all o he e ec s (e.g. idal, and non- idal aliasing e o s). The ull-noise case includes he o al e ec o all e o sou ces, including idal and non- idal aliasing e - o s. In Figs 3 and 4 , he MAGIC MRD h eshold and a ge Le el-2 ime- a ying g a i y ield p oduc equi emen s a e also plo ed. I is wo h o no e ha hese equi emen s a e adop ed om he IUGG epo (Pail e al. 2015 ), wi h he ema k ha his epo s de ines use needs ha can be ul illed by pos -p ocessed (e.g. il e ed) solu ions. The IUGG use equi emen s a e pa ially based on simula ions wi h a he op imis ic assump ions on AO backg ound model e o s, be- cause only s ochas ic e o s, bu no de e minis ic (signal- ela ed) e o componen s we e assumed. To ob ain a mo e ealis ic assess- men o he ul illmen o equi emen s, i would be also necessa y o il e he solu ions, which would educe he cumula i e e o s. As de ined abo e, his pape ollows he app oach om Haagmans & Tsaoussi ( 2020 ) in which he use equi emen s a e answe ed by mission pe o mance a Le el-2 which gua an ees consis en ace- abili y o he use needs being as close as possible o he geophysical signal o in e es , wi h he possibili y o u he sa is ying use needs ia highe le el pos -p ocessed p oduc s. The e o e, he IUGG use equi emen s compa ison agains he MAGIC pe o mance can be conside ed as conse a i e. In Figs 3 and 4 , and in simila compa - isons in his pape , pos -p ocessing was no applied in o de o a oid al e a ions in oduced by il e s, which could make he compa ison di icul o in e p e a e wa ds. The men ioned poin s he e abo e explain he b each o h eshold equi emen s a low- o-medium SH deg ees o he ull-noise case in Fig. 3 . The compa ison o he cu- mula i e e o s wi h he IUGG equi emen s shows ha in o de o Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1292 I. Da as e al . 10 20 30 40 50 60 70 80 90 100 110 120 0 50 100 150 Bende : pol. (G), incl. (N) Bende : pol. (N), incl. (N) Bende : pol. pend. 15° (G/N) Bende : incl. pend. 15° (G/N) Bende : bo h pend. 15° (G/N) pol. + sun-sync (G/N) Bende : pol. + incl. low (N/N), 5d_LL Bende : incl. low (G/N), 5d_LH in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) Bende : high o bi s (G/N), 5d_H Bende : high o bi s (N/N), 5d_H Bende : medium-high o bi s (G/N), 7d_M Bende : medium-high o bi s (N/N), 7d_M Figu e 2. Ra io o he cumula i e e o cu e o he GRACE- ype single-pai and o he ull-noise simula ed scena ios o a eco e y pe iod o 31 d. ‘High o bi s’ and ‘medium-high o bi s’ e e o 5d H and 7d M scena ios, espec i el y. The Bende scena io wi h bo h low al i ude pola and inclined pai s e e o 5d LL, while he double pai wi h low inclined pai consis s o 5d LH. The ‘15’ and ‘30’ numbe s e e o he opening angle o he pendulum o ma ion, he le ´ e ‘G’ o ‘N’ e e s o he GRACE-like and NGGM-like ACC noise assump ions. Mo e de ails abou o bi scena ios a e a ailable in Appendix A . 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bende : pol. (G), incl. (N) Bende : pol. (N), incl. (N) Bende : pol. pend. 15° (G/N) Bende : incl. pend. 15° (G/N) Bende : bo h pend. 15° (G/N) pol. + sun-sync (G/N) Bende : pol. + incl. low (N/N), 5d_LL Bende : incl. low (N/N), 5d_LH in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) Bende : high o bi s (G/N), 5d_H Bende : high o bi s (N/N), 5d_H Bende : medium-high o bi s (G/N), 7d_M Bende : medium-high o bi s (N/N), 7d_M IUGG Th eshold IUGG Ta ge Figu e 3. Cumula i e RMS cu es o he 31-d d/o 120 ull-noise nominal simula ion esul s, compa ed o he IUGG h eshold and a ge equi emen s. Fo each indi idual scena io, he mean cu e o he cumula i e RMS cu es o wo subsequen 31-d solu ions is shown. mee h eshold equi emen s and app oach a ge equi emen s, a double-pai mission is equi ed. The unce ain ies o he single-pai and pendulum o ma ions a e oo high o mee such equi emen s. The al i ude u ns ou o ha e a pa icula in luence especially o he pe o mance a mid- o-high SH deg ees. The scena ios using he 5d H o bi s (which ha e he highes sa elli e al i udes) pe - o m poo ly compa ed o 3d H scena ios. The bes pe o mance is achie ed b y 7d M and 5d LL scena ios, which a e cha ac e ized by lo w o bi al i udes. P endulum o ma ions do no p o ide a pe o - mance imp o emen wi h espec o he Bende cons ella ions, and, mo eo e , he y in oduce a highe sys em complexi y. Bende sce- na ios u ned ou o enable a ele an leap in pe o mance compa ed o all o he scena ios and o p o ide mission pe o mance which sa - is ies he MAGIC MRD equi emen s excep in he low- o-medium deg ees. E en i Figs 3 and 4 in oduce aw simula ions, al eady look- ing a cu en esul s, om a p e-ope a ional s andpoin , cu en EO-enabled se ices, such as hose o land, clima e, ocean and eme gency managemen would la gely bene i om imp o ed mass- change da a as a ailable only om a cons ella ion such as MAGIC (Masso i e al. 2022 ). Looking a he submon hly solu ions and in pa icula a 7-d solu ions (Figs 5 and 6 ), i is possible o ind a simila beha iou wi h espec o he mon hly solu ions. In o de o scale he mon hly IUGG h esholds and a ge s o sho e e ie al pe iods, he equi emen s we e scaled using a ac o s s =  31 p , (2) whe e p is he e ie al pe iod in days. In Figs 5 and 6 , o each scena io, he mean cu e o he cumula i e RMS cu es o nine Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1293 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bende : pol. (G), incl. (N) Bende : pol. (N), incl. (N) Bende : pol. pend. 15° (G/N) Bende : incl. pend. 15° (G/N) Bende : bo h pend. 15° (G/N) pol. + sun-sync (G/N) Bende : pol. + incl. low (N/N), 5d_LL Bende : incl. low (N/N), 5d_LH in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) Bende : high o bi s (G/N), 5d_H Bende : high o bi s (N/N), 5d_H Bende : medium-high o bi s (G/N), 7d_M Bende : medium-high o bi s (N/N), 7d_M IUGG Th eshold IUGG Ta ge Figu e 4. Cumula i e RMS cu es o he 31-d d/o 120 p oduc -only simula ion esul s, compa ed o he IUGG h eshold and a ge equi emen s. Fo each indi idual scena io, he mean cu e o he cumula i e RMS cu es o wo subsequen 31-d solu ions is shown. 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bende : pol. (G), incl. (N) Bende : pol. (N), incl. (N) Bende : pol. pend. 15° (G/N) Bende : incl. pend. 15° (G/N) Bende : bo h pend. 15° (G/N) pol. + sun-sync (G/N) Bende : pol. + incl. low (N/N), 5d_LL Bende : incl. low (N/N), 5d_LH in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) Bende : high o bi s (G/N), 5d_H Bende : high o bi s (N/N), 5d_H Bende : medium-high o bi s (G/N), 7d_M Bende : medium-high o bi s (N/N), 7d_M IUGG mon hly Th eshold * sq (31/7) IUGG mon hly Ta ge * sq (31/7) Figu e 5. Cumula i e RMS cu es o he 7-d d/o 120 ull-noise simula ion esul s, compa ed o he IUGG h eshold and a ge equi emen s. subsequen 7-d solu ions is p o ided. All simula ions a e gene - ally compu ed up o a maximum SH d/o o 120. Ho we e , o he 7-d single-pai simula ions, a educed d/o o 100 was used because o he educed g ound- ack co e age which would no al- low o esol e he coe icien s o la ge SH deg ees. I is e iden ha GRACE- ype single-pai 7-d Le el-2 solu ions a e domina ed by noise om SH deg ee 20 onwa ds, whe eas MAGIC scena ios o , o example, Bende in-line ype ha e an SNR o one a SH deg ee 70. The educed unce ain y o e ed by he MAGIC con- s ella ion allows o a wide use o 7-d Le el-2 ime- a ying g a - i y p oduc s e en wi h less need o pos -p ocessing by means o il e ing. 5 SCIENCE AND APPLICATIONS The pu pose o his sec ion is o desc ibe he science impac analyses o he ele an mission scena ios in di e en ields o applica ions o he mass-change da a, in pa icula in he ields o hyd ology, c yosphe e, oceanog aphy, solid Ea h, clima e change and geodesy. Sus ained g a i y ield obse a ions om space con ibu e sig- ni ican ly o a numbe o Essen ial Clima e Va iables (ECVs) as de- ined by he GCOS (Global Clima e Obse ing Sys em) p og amme. Among such a iables, sa elli e g a ime y is a unique measu emen echnique which can e ie e global-scale da a on ECVs such as ‘G oundwa e ’ and he newly adop ed ‘Te es ial Wa e S o age (TWS)’ ( h ps://gcos.wmo.in /en/essen ial- clima e- a iables/ ws ). Mo e speci ically, sa elli e g a ime y can p o ide da a se ices o he ECV p oduc s ‘G oundwa e s o age change’ and ‘TWS anomalies’. 5.1 Hy d ology One o he mos common applica ions o sa elli e g a ime y is he analysis o ime-se ies o wa e s o age a ia ions in hyd o- logical uni s such as i e basins o aqui e s. These da a p o ide undamen al in o ma ion on he s a us o wa e esou ces, on p e- condi ions and e ec s o hyd ological e x emes. Mo eo e , such da a p o ide a aluable inpu o he closu e o he wa e balance Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1294 I. Da as e al . 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bende : pol. (G), incl. (N) Bende : pol. (N), incl. (N) Bende : pol. pend. 15° (G/N) Bende : incl. pend. 15° (G/N) Bende : bo h pend. 15° (G/N) pol. + sun-sync (G/N) Bende : pol. + incl. low (N/N), 5d_LL Bende : incl. low (N/N), 5d_LH in-line single pai (G) in-line single pai (N) pend. 15° (G) pend. 30° (G) Bende : high o bi s (G/N), 5d_H Bende : high o bi s (N/N), 5d_H Bende : medium-high o bi s (G/N), 7d_M Bende : medium-high o bi s (N/N), 7d_M IUGG mon hly Th eshold * sq (31/7) IUGG mon hly Ta ge * sq (31/7) Figu e 6. Cumula i e RMS cu es o he 7-d d/o 120 p oduc -only simula ion esul s, compa ed o he IUGG h eshold and a ge equi emen s. ow a ds a comp ehensi e unde s anding o hyd olo gical sys ems in esponse o clima ic, en i onmen al and an h opogenic changes. In spi e o he unp eceden ed insigh s in o hyd ological dynamics ha a e achie ed wi h GRACE and GRACE-FO, an e en mo e widesp ead use o mass-change da a in wa e cycle s udies and wa- e esou ces assessmen s is impeded by hei low esolu ion. Fo man y w a e managemen applica ions, o ins ance, he alue o wa e s o age in o ma ion ends o inc ease wi h i s highe spa ial esolu ion and, hus, a be e ma ch wi h he size o he wa e man- agemen uni s o in e es , such as ca chmen s o aqui e s can be eached. To assess he bene i o MAGIC, 7-d simula ion ou pu s o he scena ios 3d H, 5d Ma and 5d Mb (lis ed in Appendix A ), we e compa ed o he esul s o a GRACE-like single-pai mission. Basin-a e age ime-se ies o EWH o 52 weeks we e de i ed o 405 indi idual i e basins de ined b y he Global Runo Da a Cen- e (GRDC 2020 ), ep esen ing he la ges i e basins wo ldwide. The empo al oo -mean-squa e de ia ion (RMSD) be ween he e - e ence signal (ESA ESM HI om Dobslaw e al. 2015 ) and he simula ion ime-se ies was compu ed o each i e basin o assess he accu acy o he simula ion esul s. Following he MRD a ge and h eshold alues o en isaged unce ain ies a speci ic spa ial esolu ions (Haagmans & Tsaoussi 2020 ), ha is, 400 and 260 km o he mon hly imescale in he hema ic ield o hyd ology, he SH expansions we e unca ed a he deg ee co esponding o he desi ed spa ial esolu ion, ha is, N = 50 o 400 km and N = 77 o 260 km. The co esponding h eshold unce ain ies we e de i ed om he mon hl y alues b y e o p opaga ion ollowing eq. ( 2 ). This esul ed in h esholds o 1.05 cm EWH o 400 km and 10.1 cm EWH o 260 km. In co espondence wi h chap e 4 , un il e ed so- lu ions a e used o a oid he conclusions o depend on he choice o a speci ic il e . Ho we e , i should be no ed ha unce ain ies o pos -p ocessed g a i y ield models o be la e used o hyd ological applica ions will be much smalle . Fig. 7 shows he spa ial dis ibu ion o RMSD alues o all 405 i e basins o he (a) GRACE-like mission and he MAGIC scena ios (b) 3d H, (c) 5d MA and (d) 5d Mb. The imp o emen achie ed b y he MAGIC cons ella ion is s ongl y isible. While he GRACE-like mission has maximum di e ences o mo e han 70 cm EWH o indi idual i e basins and a global a ea-weigh ed mean o 10 cm EWH, he MAGIC scena ios ha e maximum al- ues in he ange o 4–6 cm wi h a ea-weigh ed means o below 2 cm. Fu he mo e, he di e en e o cha ac e is ics o he o bi cons ella ions become e iden . The 5d Ma (i.e. a lowe inclina ion o he inclined pai compa ed o 3d H) and he 5d Mb (i.e. a lowe inclina ion o he pola pai ) scena ios appea a ou ab le o appli- ca ions in con inen al hyd ology in lowe o mid-la i udes, as hey show smalle esidual on la ge pa s o he con inen s, while he 3d H scena io pe o ms a ou ab ly in highe la i udes and pola egions. A summa y o he basin-a e age RMSD alues is p esen ed in he sca e plo in Fig. 8 ( op), in which he RMSD o each o he 405 i e basins is plo ed agains he basin size. Ho izon al lines ep esen he MRD h eshold unce ain y (1.05 cm EWH o 400 km esolu ion) and wo addi ional h esholds (2.5 and 3.5 cm EWH). The e ical blue line ep esen s he size o a sphe ical cap wi h 400 km diame e (abou 125 600 km 2 ) o oughly indica e he size o a i e basin a his spa ial esolu ion. I should be no ed ha his is only a ough app oxima ion as i e basins may la gely de ia e om a sphe ical shape. Signals o i e basins below his size a e di icul o isola e om he su oundings. I can be seen ha he unce ain y equi emen o he MRD can ha dly be ul illed by he un il e ed 7-d solu ions o any o he i e basins, including he la ges ones. Ho we e , his is no su p ising as he MRD h esholds we e in oduced o pos -p ocessed solu ions. Ne e heless, also his sca e plo again s esses he s ong imp o emen o MAGIC o e a single-pai mission. Fig. 8 (bo om) shows he a io o he RMSD o he la e compa ed o he MAGIC 3d H scena io, wi h a ios la ge han 20 especially o e y small i e basins. Fo basins a ound an ex en o 400 km, ha is, deg ee N = 50, he imp o emen by MAGIC is be ween 5 o 15 imes. Only o e y la ge i e basins, in which he addi ional smoo hing imposed by calcula ing he basin- a e age educes mos o he noise in bo h GRACE-like and MAGIC scena ios, he a io ge s smalle . Fo highe spa ial esolu ions han 260 km (i.e. unca ion a deg ee N = 77), he h eshold unce ain ies p o ided in he MRD appea o be mo e elaxed, as hey can be eached by all he MAGIC scena ios o mos i e basins (no shown). The only excep ions a e basins wi h an a ea smalle han he one co esponding o a sphe i- cal cap o 260 km diame e , which a e likely below he achie able Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1295 Figu e 7. Tempo al RMSD o basin-a e age wa e s o age a ia ions o 7-d simula ion ou pu (a: GRACE-like scena io, b: MAGIC 3d H, c: MAGIC 5d Ma and d: MAGIC 5d Mb) ela i e o he ESM HIS e e ence signal, unca ed a deg ee N = 50 (i.e. 400 km spa ial esolu ion) o 405 GRDC basins. spa ial scale. A summa y o he s a is ics o bo h spa ial esolu ions (400 and 260 km) is p o ided in Table 1 . The h eshold accu acy cu en l y gi en in he MRD o hyd olo gical applica ions a a com- pa a i el y high spa ial esolu ion (10.1 cm EWH a N = 77) can be ul illed by MAGIC 3d H (and simila ly by 5d Ma and 5d Mb) o mo e han 90 pe cen o he 405 majo i e basins wo ldwide when conside ing un il e ed solu ions. E en highe accu acies ha may be equi ed o se e al hyd ological applica ions can be me in a la ge numbe o basins (Table 1 , igh columns). In con as , he cu en MRD a he lowe spa ial esolu ion o 400 km canno be me by MAGIC o any i e basin. Howe e , elaxing his h eshold o 2.5 o 3.5 cm EWH, which can be expec ed o be s ill accep able o many hyd ological applica ions, will allow o esol ing TWS a ia ions in 67 and 90 pe cen o he in es iga ed i e basins, e- spec i el y ( c . Table 1 ). Wi h a GRACE-like mission his would no be possible, as e en o hese mo e elaxed numbe s he RMSD o almos none o he basins s ays below he h esholds. Fu he mo e, accu ac y e xpec a ions o pos -p ocessed g a i y ield solu ions a e much highe , he e o e he numbe s lis ed abo e should be ega ded as a ela i e pe o mance imp o emen and no as he inal un- ce ain ies achie ab le wi h a doub le-pai mission o hyd ological applica ions. 5.2 C yosphe e The launch o GRACE in 2002 p o ided a b eak h ough in ou un- de s anding o he glacia ed egions. Fo he i s ime, mass changes o he ice shee s and glacie s could be measu ed di ec ly, which e- ealed an imbalance o bo h ice shee s and all o he majo glacie sys ems (e.g. IMBIE 2020 , 2018 ; Ci ac ` ıe al. 2020 ; Wou e s e al. 2019 ) and p o ide an in aluable da a se o calib a ion and ali- da ion o ice shee models (e.g. Fe weis al. 2020 ; Schlegel e al. 2016 ). Despi e he majo ad ances, he e emains a s ong demand o u u e imp o emen s, o allow a ibu ion o mass signals o indi- idual glacie s and d ainage sys ems, educe signal con amina ion b y hyd olo gical and oceano g aphic mass a ia ions, and imp o e he esolu ion and accu acy o da a combina ion app oaches (e.g. wi h al ime y, GNSS and o he complimen a y da a, Pail e al. 2015 ). A u u e mission should he e o e no only con inue he cu en ime-se ies, especially ele an o he ice shee s whe e an in e play o sho and mul idecadal o cen ennial imescales is a play, bu also p o ide an inc eased spa ial esolu ion a inc eased accu acy. Al hough he GRA CE/GRA CE-FO missions p o ide us wi h a clea pic u e o he cu en imbalance o he ice shee s as whole and hei majo sub egions, many o he ele an p ocesses causing his imbalance ha e spa ial scales which emain un esol ed in he cu en space-bo ne g a ime ic obse a ions. On G eenland (G IS), mass loss occu s p edominan ly a ound he ma gins o he ice shee s. In his abla ion zone, uno o summe mel wa e ex- ceeds snow accumula ion, which is coun e ac ed by a ne mass gain in he in e io accumula ion zone. The dominan p ocesses in hese wo zones a e e y di e en om a physical poin o iew (No ¨ el e al. 2019 ). In An a c ica (AIS), he limi ed spa ial eso- lu ion p ecludes us o p ope ly sepa a e he mass changes on he eas e n and wes e n sides o he wa ming An a c ic Peninsula, and o indi idual glacie sys ems in he apidly changing Amundsen Sea Embaymen . He e, we assess he pe o mance in mass-change applica ions ela ed o he c yosphe e o di e en mission con igu a ions, ha is, he one single GRACE- ype pai scena io, and h ee Bende double- pai scena io wi h a ying al i udes and inclina ions o he pola and inclined pai (3d H, 5d Ma and 5d Mb). We ocus on he ice shee s o G IS and AIS, which we e each subdi ided in o smalle egions, based on ice p ominence, low di ec ion o he ice, and clima ological se ings. Fo AIS, he basin de ini ion o Zwally e al. ( 2012 ), was used, di iding he ice shee in o 27 egions. Fo G IS, six egions we e de ined based on Sasgen e al. ( 2012 ). In G IS, hese egions we e u he subdi ided in o he abla ion and accumula ion zone (app oxima ed using he 2000-m ele a ion con ou ), yielding 18 egions in o al. In AIS, su ace mel con ibu es minimally o Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1296 I. Da as e al . Figu e 8. Top: sca e plo o RMSD o basin a e ages o wa e s o age a ia ions o 405 GRDC i e basins unca ed a N = 50 plo ed agains basin size. Blue ho izon al lines indica e di e en unce ain y h esholds o 1.05 cm (i.e. he MRD h eshold equi emen ), 2.5 and 3.5 cm EWH. The e ical blue line ep esen s he a ea o a sphe ical cap wi h 400 km diame e . Bo om: a io o he RMSD o a GRACE-like cons ella ion e sus he RMSD o MAGIC 3d H cons ella ion o each i e basin. mass changes, hence, a simila subdi ision o he egions w as no made o his ice shee . To e ie e he mass a ia ions o he ice shee s and hei (sub) egions, wo app oaches we e used. Fi s o all, he me hod o Wou e s e al. ( 2008 ), in which he SH a e ans o med o su ace mass loading anomalies. Subsequen ly, modelled mass anomalies in he (sub) egions a e adjus ed i e a i el y, un il con e gence is eached wi h he inpu mass anomalies om he simula ion. Sec- ondly, he mascon app oach o Ran e al. ( 2018 ) syn hesizes g a i y dis u bances a p e-de ined poin s posi ioned a a speci ic sa el- li e al i ude, which a e hen con e ed in o localized mass anoma- lies h ough a linea unc ional model which uses he a iance– co a iance ma ix in i s weigh ing. Since bo h me hods yielded compa able esul s, i was decided o p oceed wi h he me hod o Wou e s e al. ( 2008 ) o compu a ional e iciency. To assess he pe o mance o he di e en mission con igu a- ions, he ime-se ies o mass a ia ions e ie ed om he simu- la ions we e compa ed o he u h signal, e ie ed om he HIS model om Dobslaw e al. ( 2015 , i.e. wi hou he noise componen , p o ided up o deg ee/o de 180). Time-se ies o all basins we e plo ed o a quali a i e assessmen . Fo a quan i a i e analysis, he oo -mean-squa e e o was compu ed based on he di e ence be- ween he simula ed and u h ime-se ies and compa ed o he ele- an h eshold and a ge use equi emen s in he MRD (Haagmans & Tsaoussi 2020 ). As o he hyd ology case s udy (Sec ion 5.1 ), he weekly, un il e ed SH expansions we e unca ed a he app op ia e deg ees N and he mon hly h eshold (5.5 and 50 cm EWH a 250 and 150 km, espec i el y) and a ge unce ain ies (0.55 and 5 cm EWH a 250 and 150 km, espec i el y) we e scaled using eq. ( 2 ). This esul s in h eshold(/ a ge ) alues o 11.6(/1.2) cm EWH a 250 km esolu ion ( N = 80), and 105(/10.5) cm a 150 km esolu- ion. Fo he la e , we use he maximum p o ided deg ee o N = 120 o he MAGIC-scena ios and N = 100 o he single GRACE- ype pai scena io. Figs 9 and 10 , and Table 2 summa ize he pe o mance o he ou con igu a ions wi h espec o he h eshold and a ge c i e ia o a spa ial esolu ion o 250 km, a mon hly imescales. Mos no able is he imp o ed pe o mance o he Bende cons ella ions wi h espec o a single-pai mission in he lowe la i ude basins o he wo ice shee s, a consequence o he addi ion o he inclined pai . Fo con- igu a ion 5d Mb, he h eshold is me o 40 ou o he 45 basins. As can be seen in Fig. 10 , basins no passing he h eshold o his con- igu a ion gene ally ha e a eas smalle han app oxima ely 62 500 (250 ×250) km 2 . On G IS, he h eshold is me o all basins, excep o he accumula ion zone o he no he nmos egion 1, whe e he RMSD is jus 1 mm abo e he h eshold. In AIS, he basins exceed- ing he h eshold a e all loca ed on he Peninsula (basins 24–27). Fo he 5d Ma and 3d H con igu a ions, he h eshold is exceeded o la ge basins, a app oxima ely 200 000 km 2 . The 3d H con ig- u a ion pe o ms sligh ly be e han 5d Ma, wi h basins 32 and 29 passing he c i e ion, espec i el y. S ill, bo h ou pe o m a single- pai GRACE-like con igu a ion (20 basins), al hough bo h hese con igu a ions esul in an inc eased RMSD in he lowe ele a ion zones o he no he nmos basins o G IS (1, 2 and 6), compa ed o he single-pai esul s (Fig. 9 ). This is a consequence o an a i ac a he ansi ion zone be ween he wo pai s o he cons ella ion cases caused by non-op imal g a i y ield eco e y p ocessing, and is a subjec o u u e in es iga ions. The e ec is ela ed o he ac ha in he ansi ion zone, going om lowe o highe la i udes, he da a densi y a ±70 ◦la i ude is changing ab up ly om a dense g ound- ack sampling o he cons ella ion o a lowe g ound- ack sampling o he pola pai . Toge he wi h di e en noise assump ions o he pola and he inclined pai , his can cause nume ical issues in he ansi ion zone. S a egies and al e na i e ela i e weigh ing schemes a e cu en ly in es iga ed o sol e his issue (Pail e al. 2022 ). When conside ing he a ge c i e ion, e y ew basins pass, none o hem loca ed on G IS. Again, he 5d Mb con igu a ion pe o ms bes , bu e en he e only 5 ou o 45 basins mee he equi emen s. When conside ing a highe spa ial esolu ion o ∼150 km (max- imum deg ee/o de 120), he RMSD inc eases o all basins o he 5d Ma cons ella ion, indica ing ha he highe coe icien s ca y li le signal in o ma ion. Fo he 5d Mb and 3d H scena ios, a e- duc ion o up o 40 pe cen RMSD is obse ed in se e al basins (AIS basins 1, 3, 8, 9, 17, 24, 25 and 26, and he G IS lowe ele a ion basin 6). When conside ing he bulk basin s a is ics, simila conclusions hold as o he 250 km esolu ion. Again, he 5d Mb con igu a ion Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1303 Figu e 15. Spec al-domain compa ison o he ea hquake signals wi h e ie al e o s in wo selec ed scena ios (GRACE-like pola only and MAGIC Bende 3d H). Top: EWH and bo om: i s adial de i a i e o he dis u bing po en ial ( T ). The spec a in bo h panels a e e xp essed in RMS pe SH de g ee, cumula i e, a nominal g ound le el ( = a WGS 84 ). due o a coseismic signal, o due o a slow aul slip, and he g a i y signal gene a ed ei he in sho ime, o de eloping a end dis- ibu ed o e ime. The noise cu e o a yea ly ime esolu ion has a deg ee a iance ha is smalle by a ac o o 2/100 compa ed o a weekly ime esolu ion, lowe ing he smalles obse able seismic momen by he ac o 0.14 (squa e oo o 2/100), which ansla es in o a momen magni ude educ ion o 0.57 due o he di e ence in momen magni ude being 2/3 ·log 10 (0.14) (Wells & Coppe smi h 1994 ). This is because he deg ee a iance o he g a i y signal scales wi h he squa e o he seismic momen . Compa ing single- and double-pai con igu a ions wi h weekly solu ions shows ha he double pai signi ican ly lowe s he de ec able momen magni ude om M 8.8 o M 8.0, and inc eases he highes obse able deg ee up o abou 60 (333 km esolu ion). Gi en a ce ain ea hquake magni ude, he highes obse able deg ee is de ined by he SNR being equal o one o highe . The highes esol able deg ee o he ea hquake depends on i s magni ude: ixing he eques ed spa ial esolu ion o an ea hquake o 333 km a weekly sam- pling, which co esponds o deg ee 60, he Bende con igu a- ion equi es he magni ude o be M 8.0, whe eas he GRACE- like con igu a ion equi es he magni ude o be M 9.2. Lowe - ing he ime esolu ion o 1 y , he Bende con igu a ion would de ec ea hquakes wi h magni ude M 7.4 upwa ds, a a spa ial esolu ion o 333 km (deg ee 60). A highe deg ees o his magni ude, he noise is expec ed o be la ge han he ea h- quake signal. Undoub edly, he MAGIC con igu a ion will b ing a de ini i e imp o emen compa ed o he p esen obse a ion echnology. Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1304 I. Da as e al . Figu e 16. Top: s anda d de ia ion o GRACE-like (le ) and MAGIC ( igh ) TWS ampli ude change o annual cycle o e 30 y . Bo om: de ec abili y o ampli ude change: colou ed pixels deno e whe e p ojec ed ampli ude change exceeds he magni ude o he accu acy. 5.5 Clima e change Some heo ies sugges ha clima e change migh lead o an ‘in en- si ica ion’ o he global wa e cycle esul ing in, o example, an inc ease in he annual ampli ude o wa e s o age change (Hun - ing on 2006 ), and/o ha clima e-induced changes in a mosphe ic ci cula ion pa e ns a ec he phase o annual peaks (Dunning e al. 2018 ). Jensen e al. ( 2020 ) in es iga ed he de ec abili y o ne TWS changes in he annual wa e cycle using sa elli e g a ime y. A sa el- li e mission able o obse e and quan i y hese changes would be bene icial in wo ways: (i) sa elli e g a i y could be used as ool o p oo (o alsi y) he pos ula e o an in ensi ica ion o he wa- e cycle in di e en egions o he wo ld, and (2) he da a could se e o alida e whe he clima e models co ec ly simula e such changes. Jensen e al. ( 2020 ) compu ed p ojec ed changes in am- pli ude ( ig. 7 a o Jensen e al. 2020 ) and phase ( ig. 8 a o Jensen e al. 2020 ) de i ed om an ensemble o global clima e models aking pa in he CMIP6 model in e compa ison p ojec (Ey ing e al. 2016 ). To analyse he de ec abili y o hese p ojec ed changes o he annual cycle by cu en o u u e sa elli e g a ime y missions, hey we e compa ed o he achie able accu acies o hese quan i ies om he GRACE-like and he MAGIC 3d H simula ion ou pu ollowing he me hodology used in Jensen e al. ( 2020 ). To his end, he g id- wise RMSD alues o he simula ed 7-d empo al esiduals we e e o p opaga ed o de i e s anda d de ia ions o ampli ude/phase change a e 30 y . Fo he ampli ude change, hese s anda d de- ia ions a e shown in Fig. 16 ( op) o he GRACE-like (le ) and o he MAGIC ( igh ) scena ios. He e, VADER il e ed solu ions (Ho a h e al. 2018 ) a e used applying a ela i el y weak il e ( α= 10), as he un il e ed simula ion ou pu ha was used in he abo e chap e s is no sui able o he de ec ion o hese small changes. The p ojec ed ampli ude changes ( om Jensen e al. 2020 ) a e now challenged agains hese unce ain ies and colou ed pixels in Fig. 16 (bo om) deno e egions whe e he p ojec ed ampli ude change ex- ceeds he magni ude o he unce ain y. While, acco ding o he simula ions a hand, a GRACE-like scena io can only de ec he an icipa ed ampli ude changes in 36 pe cen o he land a ea a e 30 y o obse a ion, MAGIC-like scena io would be able o iden- i y such changes in 64 pe cen o he land a ea. Rega ding changes in he annual phase, a de ec abili y o a 30-y phase change om he single-pai scena io can be iden i ied in 30 pe cen o he land a ea and a signi ican inc ease o his po ion (56 pe cen o land a ea) o he MAGIC scena io. 6 CONCLUSIONS AND RECOMMENDATIONS The in es iga ions p esen ed in his pape ha e demons a ed he su- pe io pe o mance o Bende double-pai in-line mission concep s o e o he po en ial cons ella ion a chi ec u es, such as single-pai inline, SSO, o pendulum. As o all g a i y missions, he al i ude emains he main pe o mance d i e . In case o MAGIC, a low al i ude oge he wi h a high-pe o mance ins umen a ion o he in- clined pai was shown o be c ucial in sa is ying he use needs. The Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 MAGIC expec ed impac on science and applica ions 1305 compa ison o he cumula i e e o s wi h he IUGG use equi e- men s once again con i med ha o mee h eshold equi emen s and app oach a ge equi emen s, a Bende double-pai mission is equi ed. The educed unce ain y o e ed by he MAGIC cons el- la ion allows o a wide use o 7-d Le el-2 ime- a ying g a i y p oduc s e en wi h less need o pos -p ocessing by means o il e - ing. An in e compa ison o MAGIC and GRACE- ype scena ios was pe o med by means o Le el-2 syn he ic p oduc s, consis en wi h he app oach on answe ing use equi emen s and o wa d-looking o a u u e mass-change p oduc wi h less need o pos -p ocessing. The analyses o MAGIC scena ios o di e en applica ion a eas in he ield o geosciences con i med ha he double-pai con igu a ion will signi ican ly enla ge he numbe o obse able mass-change phenomena by esol ing smalle spa ial scales wi h su icien accu- acy. In his way, also hi he o indisce nible Ea h sys em p ocesses can be un a elled and quan i ied wi h he MAGIC cons ella ion. Fo hyd ological applica ions, he MAGIC cons ella ion will p o- ide a signi ican added alue because he numbe o hyd ological uni s such as i e basins o aqui e s ha can be analysed o wa e s o age a ia ions wi h ce ain accu acy equi emen s will ma kedly inc ease compa ed o a GRACE-like mission. Fo un il e ed solu- ions, he h eshold accu acy o 10.1 cm EWH gi en in he cu en MRD a high spa ial esolu ion (260 km) can be ul illed by he analysed double-pai scena ios o mo e han 90 pe cen o he i e basins wo ldwide, whe eas a he lowe spa ial esolu ion o 400 km, he MRD h eshold accu acy may need o be elaxed o 2.5 o 3.5 cm EWH o esol e TWS a ia ions in 67 and 90 pe cen o he in es iga ed i e basins, espec i el y. The p oposed MAGIC double-pai con igu a ions will signi i- can ly imp o e ou abili y o moni o mass displacemen s on he ice shee s compa ed o wha is cu en ly possible. Fo example, ou esul s show ha i should become easible o sepa a e mass-change signals in he in e io o G IS om hose in he coas al zones, and esol e small-scale mass a ia ions in challenging egions such as he AIS Peninsula. The 5d Mb con igu a ion shows he bes pe - o mance o he c yosphe e applica ions e alua ed he e, wi h he la ges numbe o egions o G IS and AIS passing he h eshold and a ge c i e ia o he cu en MRD. Fo oceanog aphy, he ob ained esul s also con i med ha he MAGIC double-pai con igu a ions p oduce a g ea imp o emen in ocean bo om p essu e de e mina ion o e a single pai GRACE-like con igu a ion. By ex ending o SH deg ees ha pe mi clea physical in e p e a ion up o be ween deg ee 50 and abou 80, depending on he signal, he e is he po en ial o moni o MOC changes on imescales o yea s and decades. Fo he Ca ibbean Sea example analysed he e, i is shown ha hi he o ba ely de ec able signals o abou 1 cm EWH RMS a iabili y become de ec able and wi h op imiza ion o me hods, he MAGIC con igu a ion is expec ed o be able o explain 80–90 pe cen o i s a iance. Compa ing weekly solu ions o single- and double-pai con ig- u a ions, i was shown ha MAGIC will signi ican ly lowe he de ec able ea hquake momen magni ude om M 8.8 o M 8.0, and inc ease he highes obse able deg ee up o abou 60 (333 km esolu ion). Lowe ing he ime esolu ion o 1 y , he Bende con- s ella ion would be able o de ec ea hquakes wi h magni ude M 7.4 upwa ds, a he same spa ial esolu ion o 333 km. Unde he clima e change hema ic ield, a GRACE-like mission can only de ec he an icipa ed ampli ude changes in 36 pe cen o he land a ea a e 30 y o obse a ion. MAGIC u ned ou be able o iden i y such changes in 64 pe cen o he land a ea. Fo changes in he annual phase, a de ec abili y o a 30-y phase change om he single-pai scena io can be again iden i ied in only 30 pe cen o he land a ea, while MAGIC enables a de ec abili y o e 56 pe cen o land a ea. These p omising esul s in a ious applica ions ields demon- s a e, ha MAGIC will ha e g ea po en ial o li mass anspo moni o ing om space o a nex le el. As al eady men ioned in In- oduc ion, one o he main goals o MAGIC will be o p o ide also sho - e m ( as - ack) p oduc s wi h sho la ency o ope a ional se ice applica ions, such as d ough and lood moni o ing and p e- dic ion, and wa e managemen . The expec ed impac o MAGIC in his domain is cu en ly being in es iga ed and quan i ied, and ela ed impac s udies will be pa o u u e wo k. ACKNOWLEDGMENTS This main wo k p esen ed in his pape was pe o med in he amewo k o he p ojec ‘NGGM/MAGIC—SCIENCE SUP- PORT STUDY DURING PHASE A’, ESA-ESTEC, Con ac 4000134613/21/NL/FF/ab unded by he Eu opean Space Agency. The au ho s would like o hank he membe s o he conso ium s udy o hei con ibu ion. DATA AVAILABILITY The Le el-2 g a i y ield simula ed da a used in his publica ion a e eely a ailable on he In e na ional Cen e o Global Ea h Models (ICGEM) websi e: h p://icgem.g z-po sdam.de/sl/simula ed, and shall be ci ed as Da as e al. ( 2023 ). 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Wha can we expec om he inclined sa elli e o ma ion o empo al g a i y ield de e mina ion?, Su . Geophys., 42 (3), 699–726, Sp inge Science and Business Media LLC, doi:10.1007/s10712-021- 09641-9. Downloaded om h ps://academic.oup.com/gji/a icle/236/3/1288/7473715 by Uni e si ae Hambu g use on 01 Feb ua y 2024 1308 I. Da as e al . APPENDIX A: MAGIC ORBIT SCENARIOS O bi s se s o inclined (IP o P2) and pola (PP o P1) pai s. The ID shows he numbe o subcycle days o which he se is op imized and an addi ional in o ma ion abou he al i udes: (M)id, (H)igh. No e ha he semimajo axis is educed by 6378 km o highligh ing di e ences in al i ude. The o he columns p o ide in o ma ion abou he homogenei y, longi ude shi and sub-cycles o he g ound- ack pa e ns; mo e de ails a e desc ibed in Masso i e al. ( 2021 ) and Haagmans & Tsaoussi ( 2020 ). Table A1. O bi design pa ame e s o cons ella ion se s including inclined (IP o P2) and pola (PP o P1) pai s. ID IP Al . [km] IP Inc. [ ◦] PP Al . [km] PP Inc. [ ◦] hl IP [-] hl PP [-] Lon. shi IP [ ◦] Lon. shi PP [ ◦] Subcycles [d] 3d M 409 70 440 89 1.368 1.383 2.308 2.384 2, 3, 8, 11, 30 3d H 432 70 463 89 1.451 1.449 −3.076 −3.067 3, 7, 31 5d Ma 396 65 434 89 1.397 1.383 −1.499 −1.458 2, 3, 5, 13, 18, 31 5d Mb 397 70 425 87 1.168 1.167 0.736 0.733 2, 5, 27, 32 5d H 465 75 488 89 1.185 1.190 0.762 0.781 4, 5, 29 7d M 389 70 417 87 1.238 1.253 0.743 0.786 2, 7, 30 7d H 432 70 463 89 1.218 1.226 0.672 0.692 3, 7, 31 SSO o 3d H 477 97 463 89 1.454 1.449 −3.097 −3.067 3, 7, 31 SSO o 7d H 477 97 463 89 1.201 1.226 0.622 0.692 3, 7, 31 5d LL 344 70 376 89 1.423 1.410 −1.671 −1.628 1, 2, 5, 12, 29 5d LH 344 71.5 492 89 1.169 1.172 −0.732 −0.790 5, (32-31) U3d5d H 432 70 492 89 1.451 (3d) 1.172 (5d) −3.076 (3d) −0.790 (5d) IP: 3, 31; PP: 5, 31 U5d H 460 70 492 89 1.061 (5d) 1.172 (5d) −0.284 (5d) −0.790 (5d) IP: 5; PP: 5, 31 U3d H 402 65 463 89 1.382 1.449 2.380 −3.067 IP: 3, 29-30; PP: 3, 7, 31 C The Au ho (s) 2024. 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